The embodiments described herein relate generally to simulation modeling and, more particularly, to simulating hydraulic fracture in rocks and modeling fluid flow in the life sciences.
Hydraulic fracturing (commonly referred to as “fracking”) is the process of initiation and propagation of an underground crack by pumping fluid at relatively high flow rates and pressures. Hydraulic fracturing is desired for a variety of reasons, including enhanced oil and gas recovery deep below the earth. Field data from hydraulic fracturing operations exist primarily in the form of pressure response curves. It is difficult to define the actual hydraulic fracture geometry from this data alone. Therefore, analytical solutions and numerical simulations are used to evaluate and predict the location, direction, and extent of these hydraulic fractures.
Early simplified theoretical models for hydraulic fracturing use an elasticity plane strain crack solution to establish the so-called PK model. Other attempted solutions have used significant amount of research to obtain analytical solutions for different cases. However, as the analytical model and the empirical approaches cannot handle fractures of arbitrary shape and orientations, a fully three-dimensional (3D) hydraulic fracture simulator is vital to the petroleum industry.
One such simulator is a fully-3D fracture analysis code, called FRANC3D, developed at Cornell University and based on remeshing and updating the boundary conditions for each stage of crack growth. However, FRANC3D is based on linear elastic fracture mechanics (LEFM), which generally gives reasonable predictions for hard (brittle) rock hydraulic fractures. However, for ductile rocks, such as clay or weakly consolidated sandstones (low cohesion granular material), LEFM-based methods typically give conservative predictions on fracture geometry because the ductile fracture process zone ahead of the crack is not considered. In addition, FRANC3D neglects the fluid continuity equation in the medium surrounding the fracture.
Some known simulation products use pore pressure cohesive zone model (CZM) to account for rock ductility (such as ductile shale) as well as fluid flow continuity. Such technology has been applied to predict hydraulic fracturing with different rock properties for injection wells by oil and gas companies. However, the crack path has to be predefined or be aligned with the element edge when using the pore pressure cohesive elements.
Accordingly, modeling hydraulic fracture requires that the crack initiates and propagates along an arbitrary, solution-dependent path. One drawback of conventional methods is that mesh is required to conform to the geometric discontinuities. Modeling a growing crack is more cumbersome because the mesh must be updated continuously to match geometry of the discontinuity as the crack progress. Moreover, using cohesive elements is limited in that cohesive elements must align with underlying element boundaries and the cracks propagate along a set of predefined paths.